This volume contains a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in Bethlehem, Pennsylvania, USA on July 30-August 1, 2012. The conference brought together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. Topics presented included algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and addressed the application of optimization techniques in finance, logistics, health, and other important fields. The contributions contained in this volume represent a sample of these topics and applications and illustrate the broad diversity of ideas discussed at the meeting.

This book explores various renewal processes in the context of probability theory, uncertainty theory and chance theory. It also covers the applications of these renewal processes in maintenance models and insurance risk models. The methods used to derive the limit of the renewal rate, the reward rate, and the availability rate are of particular interest, as they can easily be extended to the derivation of other models. Its comprehensive and systematic treatment of renewal processes, renewal reward processes and the alternating renewal process is one of the book's major features, making it particularly valuable for readers who are interested in learning about renewal theory. Given its scope, the book will benefit researchers, engineers, and graduate students in the fields of mathematics, information science, operations research, industrial engineering, etc.

The purpose of this contributed volume is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The book presents information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in mathematical analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces. The level of exposition is directed to a wide audience, including students and established researchers. Key topics covered include Banach contraction theorem, hyperconvex metric spaces, modular function spaces, fixed point theory in ordered sets, topological fixed point theory for set-valued maps, coincidence theorems, Lefschetz and Nielsen theories, systems of nonlinear inequalities, iterative methods for fixed point problems, and the Ekeland's variational principle.

Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion "Samuelson" market model (also known as the Black-Scholes model because it is used in that most famous theory), instead opting for models that allowed minimax approaches to complement or replace stochastic methods. Among the most fruitful models were those utilizing game-theoretic tools and the so-called interval market model. Over time, these models have slowly but steadily gained influence in the financial community, providing a useful alternative to classical methods. A self-contained monograph, The Interval Market Model in Mathematical Finance: Game-Theoretic Methods assembles some of the most important results, old and new, in this area of research. Written by seven of the most prominent pioneers of the interval market model and game-theoretic finance, the work provides a detailed account of several closely related modeling techniques for an array of problems in mathematical economics. The book is divided into five parts, which successively address topics including: * probability-free Black-Scholes theory; * fair-price interval of an option; * representation formulas and fast algorithms for option pricing; * rainbow options; * tychastic approach of mathematical finance based upon viability theory. This book provides a welcome addition to the literature, complementing myriad titles on the market that take a classical approach to mathematical finance. It is a worthwhile resource for researchers in applied mathematics and quantitative finance, and has also been written in a manner accessible to financially-inclined readers with a limited technical background.

The present volume contains invited talks of 11th biennial conference on "Emerging Mathematical Methods, Models and Algorithms for Science and Technology". The main message of the book is that mathematics has a great potential to analyse and understand the challenging problems of nanotechnology, biotechnology, medical science, oil industry and financial technology. The book highlights all the features and main theme discussed in the conference. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world.

"Networks of Echoes: Imitation, Innovation and Invisible Leaders" is a mathematically rigorous and data rich book on a fascinating area of the science and engineering of social webs. There are hundreds of complex network phenomena whose statistical properties are described by inverse power laws. The phenomena of interest are not arcane events that we encounter only fleetingly, but are events that dominate our lives. We examine how this intermittent statistical behavior intertwines itself with what appears to be the organized activity of social groups. The book is structured as answers to a sequence of questions such as: How are decisions reached in elections and boardrooms? How is the stability of a society undermined by zealots and committed minorities and how is that stability re-established? Can we learn to answer such questions about human behavior by studying the way flocks of birds retain their formation when eluding a predator? These questions and others are answered using a generic model of a complex dynamic network one whose global behavior is determined by a symmetric interaction among individuals based on social imitation. The complexity of the network is manifest in time series resulting from self-organized critical dynamics that have divergent first and second moments, are non-stationary, non-ergodic and non-Poisson. How phase transitions in the network dynamics influence such activity as decision making is a fascinating story and provides a context for introducing many of the mathematical ideas necessary for understanding complex networks in general. The decision making model (DMM) is selected to emphasize that there are features of complex webs that supersede specific mechanisms and need to be understood from a general perspective. This insightful overview of recent tools and their uses may serve as an introduction and curriculum guide in related courses."

This proceedings volume addresses advances in global optimization a multidisciplinary research field that deals with the analysis, characterization and computation of global minima and/or maxima of nonlinear, non-convex and nonsmooth functions in continuous or discrete forms. The volume contains selected papers from the third biannual World Congress on Global Optimization in Engineering & Science (WCGO), held in the Yellow Mountains, Anhui, China on July 8-12, 2013. The papers fall into eight topical sections: mathematical programming; combinatorial optimization; duality theory; topology optimization; variational inequalities and complementarity problems; numerical optimization; stochastic models and simulation and complex simulation and supply chain analysis."

Combining control theory and modeling, this textbook introduces and builds on methods for simulating and tackling concrete problems in a variety of applied sciences. Emphasizing "learning by doing," the authors focus on examples and applications to real-world problems. An elementary presentation of advanced concepts, proofs to introduce new ideas, and carefully presented MATLAB(r) programs help foster an understanding of the basics, but also lead the way to new, independent research.

With minimal prerequisites and exercises in each chapter, this work serves as an excellent textbook and referencefor graduate and advanced undergraduatestudents, researchers, and practitioners in mathematics, physics, engineering, computer science, as well as biology, biotechnology, economics, and finance."

Maximizing reader insights into the interactions between game theory, excessive crowding and safety and security elements, this book establishes a new research angle by illustrating linkages between different research approaches and through laying the foundations for subsequent analysis. Congestion (excessive crowding) is defined in this work as all kinds of flows; e.g., road/sea/air traffic, people, data, information, water, electricity, and organisms. Analysing systems where congestion occurs - which may be in parallel, series, interlinked, or interdependent, with flows one way or both ways - this book puts forward new congestion models, breaking new ground by introducing game theory and safety/security into proceedings. Addressing the multiple actors who may hold different concerns regarding system reliability; e.g. one or several terrorists, a government, various local or regional government agencies, or others with stakes for or against system reliability, this book describes how governments and authorities may have the tools to handle congestion, but that these tools need to be improved whilst additionally ensuring safety and security against various threats. This game-theoretic analysis sets this book apart from the current congestion literature and ensures that the book will be of use to postgraduates, researchers, 3rd/4th-year undergraduates, policy makers, and practitioners.

This book presents new optimization approaches and methods and their application in real-world and industrial problems, and demonstrates how many of the problems arising in engineering, economics and other domains can be formulated as optimization problems. Constituting a comprehensive collection of extended contributions from the 9th International Workshop on Computational Optimization (WCO) held in Gdansk, Poland, September 11-14, 2016, the book discusses important applications such as job scheduling, wildfire modeling, parameter settings for controlling different processes, capital budgeting, data mining, finding the location of sensors in a given network, identifying the conformation of molecules, algorithm correctness, decision support system, and computer memory management. Further, it shows how to develop algorithms for these based on new intelligent methods like evolutionary computations, ant colony optimization and constraint programming. The book is a valuable resource for researchers and practitioners alike.

This book reports the latest findings on intelligent energy management of Internet data centers in smart-grid environments. The book gathers novel research ideas in Internet data center energy management, especially scenarios with cyber-related vulnerabilities, power outages and carbon emission constraints. The book will be of interest to university researchers, R&D engineers and graduate students in communication and networking areas who wish to learn the core principles, methods, algorithms, and applications of energy management of Internet data centers in smart grids.

This book provides an analysis of strategic behavior in international crises. Various aspects of crisis decision and interaction, such as initiation, misperception, deception, learning, and termination, are studied by means of a game model that incorporates psychological variables. This integrative approach is designed to narrow the gap between psychological and game-theoretical studies of crisis, which are generally considered to be incompatible. The utility of the approach is demonstrated by means of an in-depth case study of the 1967 Middle East crisis. This study will be of interest to scholars in political science and international relations and political science, crisis theory, and game theory.

This book presents the latest research advances in complex network structure analytics based on computational intelligence (CI) approaches, particularly evolutionary optimization. Most if not all network issues are actually optimization problems, which are mostly NP-hard and challenge conventional optimization techniques. To effectively and efficiently solve these hard optimization problems, CI based network structure analytics offer significant advantages over conventional network analytics techniques. Meanwhile, using CI techniques may facilitate smart decision making by providing multiple options to choose from, while conventional methods can only offer a decision maker a single suggestion. In addition, CI based network structure analytics can greatly facilitate network modeling and analysis. And employing CI techniques to resolve network issues is likely to inspire other fields of study such as recommender systems, system biology, etc., which will in turn expand CI's scope and applications. As a comprehensive text, the book covers a range of key topics, including network community discovery, evolutionary optimization, network structure balance analytics, network robustness analytics, community-based personalized recommendation, influence maximization, and biological network alignment. Offering a rich blend of theory and practice, the book is suitable for students, researchers and practitioners interested in network analytics and computational intelligence, both as a textbook and as a reference work.

This book presents powerful techniques for solving global optimization problems on manifolds by means of evolutionary algorithms, and shows in practice how these techniques can be applied to solve real-world problems. It describes recent findings and well-known key facts in general and differential topology, revisiting them all in the context of application to current optimization problems. Special emphasis is put on game theory problems. Here, these problems are reformulated as constrained global optimization tasks and solved with the help of Fuzzy ASA. In addition, more abstract examples, including minimizations of well-known functions, are also included. Although the Fuzzy ASA approach has been chosen as the main optimizing paradigm, the book suggests that other metaheuristic methods could be used as well. Some of them are introduced, together with their advantages and disadvantages. Readers should possess some knowledge of linear algebra, and of basic concepts of numerical analysis and probability theory. Many necessary definitions and fundamental results are provided, with the formal mathematical requirements limited to a minimum, while the focus is kept firmly on continuous problems. The book offers a valuable resource for students, researchers and practitioners. It is suitable for university courses on optimization and for self-study.

This volume presents five surveys with extensive bibliographies and six original contributions on set optimization and its applications in mathematical finance and game theory. The topics range from more conventional approaches that look for minimal/maximal elements with respect to vector orders or set relations, to the new complete-lattice approach that comprises a coherent solution concept for set optimization problems, along with existence results, duality theorems, optimality conditions, variational inequalities and theoretical foundations for algorithms. Modern approaches to scalarization methods can be found as well as a fundamental contribution to conditional analysis. The theory is tailor-made for financial applications, in particular risk evaluation and [super-]hedging for market models with transaction costs, but it also provides a refreshing new perspective on vector optimization. There is no comparable volume on the market, making the book an invaluable resource for researchers working in vector optimization and multi-criteria decision-making, mathematical finance and economics as well as [set-valued] variational analysis.

This book presents the works and research findings of physicists, economists, mathematicians, statisticians, and financial engineers who have undertaken data-driven modelling of market dynamics and other empirical studies in the field of Econophysics. During recent decades, the financial market landscape has changed dramatically with the deregulation of markets and the growing complexity of products. The ever-increasing speed and decreasing costs of computational power and networks have led to the emergence of huge databases. The availability of these data should permit the development of models that are better founded empirically, and econophysicists have accordingly been advocating that one should rely primarily on the empirical observations in order to construct models and validate them. The recent turmoil in financial markets and the 2008 crash appear to offer a strong rationale for new models and approaches. The Econophysics community accordingly has an important future role to play in market modelling. The Econophys-Kolkata VIII conference proceedings are devoted to the presentation of many such modelling efforts and address recent developments. A number of leading researchers from across the globe report on their recent work, comment on the latest issues, and review the contemporary literature.

This book on constrained optimization is novel in that it fuses these themes: * use examples to introduce general ideas; * engage the student in spreadsheet computation; * survey the uses of constrained optimization;. * investigate game theory and nonlinear optimization, * link the subject to economic reasoning, and * present the requisite mathematics. Blending these themes makes constrained optimization more accessible and more valuable. It stimulates the student's interest, quickens the learning process, reveals connections to several academic and professional fields, and deepens the student's grasp of the relevant mathematics. The book is designed for use in courses that focus on the applications of constrained optimization, in courses that emphasize the theory, and in courses that link the subject to economics.

This unified volume is a collection of invited chapters presenting recent developments in the field of data analysis, with applications to reliability and inference, data mining, bioinformatics, lifetime data, and neural networks. The book is a useful reference for graduate students, researchers, and practitioners in statistics, mathematics, engineering, economics, social science, bioengineering, and bioscience.

Mathematical optimization encompasses both a rich and rapidly evolving body of fundamental theory, and a variety of exciting applications in science and engineering. The present book contains a careful selection of articles on recent advances in optimization theory, numerical methods, and their applications in engineering. It features in particular new methods and applications in the fields of optimal control, PDE-constrained optimization, nonlinear optimization, and convex optimization. The authors of this volume took part in the 14th Belgian-French-German Conference on Optimization (BFG09) organized in Leuven, Belgium, on September 14-18, 2009. The volume contains a selection of reviewed articles contributed by the conference speakers as well as three survey articles by plenary speakers and two papers authored by the winners of the best talk and best poster prizes awarded at BFG09. Researchers and graduate students in applied mathematics, computer science, and many branches of engineering will find in this book an interesting and useful collection of recent ideas on the methods and applications of optimization.

The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash's legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.

The advent of rapid, reliable and cheap computing power over the last decades has transformed many, if not most, fields of science and engineering. The multidisciplinary field of optimization is no exception. First of all, with fast computers, researchers and engineers can apply classical optimization methods to problems of larger and larger size. In addition, however, researchers have developed a host of new optimization algorithms that operate in a rather different way than the classical ones, and that allow practitioners to attack optimization problems where the classical methods are either not applicable or simply too costly (in terms of time and other resources) to apply. This book is intended as a course book for introductory courses in stochastic optimization algorithms (in this book, the terms optimization method and optimization algorithm will be used interchangeably), and it has grown from a set of lectures notes used in courses, taught by the author, at the international master programme Complex Adaptive Systems at Chalmers University of Technology in Goteborg, Sweden.Thus, a suitable audience for this book are third and fourth-year engineering students, with a background in engineering mathematics (analysis, algebra, and probability theory) as well as some knowledge of computer programming.

This book integrates multiple criteria concepts and methods for problems within the Risk, Reliability and Maintenance (RRM) context. The concepts and foundations related to RRM are considered for this integration with multicriteria approaches. In the book, a general framework for building decision models is presented and this is illustrated in various chapters by discussing many different decision models related to the RRM context. The scope of the book is related to ways of how to integrate Applied Probability and Decision Making. In Applied Probability, this mainly includes: decision analysis and reliability theory, amongst other topics closely related to risk analysis and maintenance. In Decision Making, it includes a broad range of topics in MCDM (Multi-Criteria Decision Making) and MCDA (Multi-Criteria Decision Aiding; also known as Multi-Criteria Decision Analysis). In addition to decision analysis, some of the topics related to Mathematical Programming area are briefly considered, such as multiobjective optimization, since methods related to these topics have been applied to the context of RRM. The book addresses an innovative treatment for the decision making in RRM, thereby improving the integration of fundamental concepts from the areas of both RRM and decision making. This is accomplished by presenting an overview of the literature on decision making in RRM. Some pitfalls of decision models when applying them to RRM in practice are discussed and guidance on overcoming these drawbacks is offered. The procedure enables multicriteria models to be built for the RRM context, including guidance on choosing an appropriate multicriteria method for a particular problem faced in the RRM context. The book also includes many research advances in these topics. Most of the multicriteria decision models that are described are specific applications that have been influenced by this research and the advances in this field. Multicriteria and Multiobjective Models for Risk, Reliability and Maintenance Decision Analysis is implicitly structured in three parts, with 12 chapters. The first part deals with MCDM/A concepts methods and decision processes. The second part presents the main concepts and foundations of RRM. Finally the third part deals with specific decision problems in the RRM context approached with MCDM/A models.

Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences.

This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovi, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational algorithms, and multidisciplinary applications.

Special features of this volume:

- Presents results and approximation methods in various computational settings including: polynomial and orthogonal systems, analytic functions, and differential equations.

- Provides a historical overview of approximation theory and many of its subdisciplines;

- Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences.

"Approximation and Computation" is intended for mathematicians and researchers focusing on approximation theory and numerical analysis, but can also be a valuable resource to students and researchers in the computational and applied sciences."